If you will be living alone, and are a pretty simple person, you may consider some of the small office spaces right in the Financial District. You'll need the bathroom key. And have to lie about your purpose in renting the space, but it's cheaper than anywhere else within miles.
Otherwise, decide if you are going to rent or buy.
There are plenty of affordable rentals in the Gold Coast, where you could walk during the summer to the financial district. If you are buying, there are very affordable older condos in Lincoln Park. And if you want a house, you should check out Bridgeport or Pilsen, otherwise go further north to Portage Park or Jefferson Park. And then, you may like a multi-unit (multi family) like a two flat or a three flat. That will open up more areas for you.
Your best bet is to talk with a good loan officer to see what your options are. Only after looking into everything will they know what they can or cannot approve you for. If you need a good loan officer, I would be happy to recommend you one.
Americorp Real Estate
Brokers Associate, e-PRO
Contact Mike Del Preto of Hartland Mortgage through his website at http://www.mikedelpreto.com. He is extremely knowledgeable and experienced with doing refi's in Chicago where the owner wants to switch to FHA. Many lenders will say they have the experience but I can personally guarantee that Mike does.